The Legacy Of A 75 Year Old Problem.

[nakulgupta 0]

Mathematical genius Srinivasa Ramanujan devised the problem and after 75 years Karl Mahlburg of the University of Wiscinson, Madison, USA solved it in a few months. So what was the problem? Well, here it goes:Lets take the number 5. In how many ways can you show that 5 is the sum of other smaller numbers?5 = 55 = 1 + 1 + 1 + 1 + 15 = 4 + 15 = 3 + 25 = 2 + 2 + 15 = 1 + 3 + 15 = 2 + 1 + 1+ 1Hence, the number of ways is 7.This property of numbers is called partitions and is written as p(5) = 7.Now comes the fun part, these partitions comes in intriguing pairs. For instance, p(15)=176. From the 176 ways it can be partitioned, a pair of sums can be5 + 4 + 3 + 1 + 1 + 1and6 + 3 + 3 + 2 +1If this is assembled in a grid like pattern, if you read downwards you will get the second pattern where if you read across you will get the first pattern.Another interesting thing that Ramanujan and Hardy found while working in the UK on partitions is that numbers of the order 5n + 4 are divisible by 5 and numbers of the order 7n + 4 are divisible for 7. The most fascinating part of this is ofcourse the fact that all these are prime numbers (order in chaos, no doubt). This was given a name: congruences. The question that hovered after this discovery is whether all the primes followed this property and why. If not, why only some of this.The next in the family of primes was ofcourse 11 and congruence for that was found by Andrews and Prof. Garavan of the University of Florida. They called it “crank”. Recently, Prof. Ken Ono stumbled across Ramanujan’s notebook and found that the patterns of congruence was just the tip of the iceberg, there were patterns everywhere.Mahlburg wanted to continue Prof Ono’s work on congruence and so he did to prove why the “crank” rule applied to all prime numbers. He submitted two papers called the ‘The Andrews-Garvan-Dyson crank and proofs of partition congruences’ and ‘More congruences for the coefficients of quotients of Eisenstein series’ to The Journal of Number Theory proving that the “crank” theory existed for all prime numbers.So why is his work so important to the common person? Well, it is so because Websites use the laws of partitions to encrypt credit card information sent over the Internet. Mahlburg’s finding would only make it more secure. So the next time you pay for your webhosting, you know whom to thank!

[adeydas 0]

dued, you could have atleast told me before copying it from my site. anyways i'm not blogging anymore so i guess it hardly matters.

[JUDGE_RELIC 0]

Does it really matter, you probably copied it as well, it's still interesting.

[GameUltra 0]

Even so if he copied it from another site you still posted it as you own without using quotes, so you will still not recieve credits for it when you go to apply for hosting.

[yordan 10]

Even so if he copied it from another site you still posted it as you own without using quotes, so you will still not recieve credits for it when you go to apply for hosting.

That's another funny study. Let's now study a nice mathematical property of relationships, which name is "transitivity". For instance, if I'm taller than you and you're taller than your brother, then I'm taller than your brother.
And now let's study the transititivity of the "stealing" relatioship.
Of course, copying from another person is stealing if you don't quote and mention the real author, because it violates the intellectual property of the author.
And now comes the mathematical relashionship. Is this a transitive relationship ? If yes, stealing a stealer is stealing.
By the way, if you thind that what I'm writing is quite stupid, you are right.
And if you think that I copied this from somebody else, you are wrong. I decided, from my own authority, to do this demonstration and to use the "stealer" study case as an example of a well known group theory. These are my own words, and looking if the relationship is transitive is in fact a very important process in knowing if we are really talking about the mathematical identity named "a group" : if the relationship is not transitive, my set of people is not a group linked by the "steal" relationship.
Isn't this nice, where mathematics and sociology come together ? But this is another Story, and Isaac Asimov wrote a lot about mathematical predictions of human behaviour.

[Vicious_AD 0]

That's another funny study. Let's now study a nice mathematical property of relationships, which name is "transitivity". For instance, if I'm taller than you and you're taller than your brother, then I'm taller than your brother.And now let's study the transititivity of the "stealing" relatioship.
Of course, copying from another person is stealing if you don't quote and mention the real author, because it violates the intellectual property of the author.
And now comes the mathematical relashionship. Is this a transitive relationship ? If yes, stealing a stealer is stealing.
By the way, if you thind that what I'm writing is quite stupid, you are right.
And if you think that I copied this from somebody else, you are wrong. I decided, from my own authority, to do this demonstration and to use the "stealer" study case as an example of a well known group theory. These are my own words, and looking if the relationship is transitive is in fact a very important process in knowing if we are really talking about the mathematical identity named "a group" : if the relationship is not transitive, my set of people is not a group linked by the "steal" relationship.
Isn't this nice, where mathematics and sociology come together ? But this is another Story, and Isaac Asimov wrote a lot about mathematical predictions of human behaviour.

Bravo on the flowery way of saying "two wrongs don't make a right"